CN104234046B - Consider the high-pressure rotary jet grouting pile method for determining diameter of whole construction parameter and soil strength variation - Google Patents

Abstract

The invention provides a kind of high-pressure rotary jet grouting pile method for determining diameter considering whole construction parameter and soil strength variation, comprise: the first step, construction field geology survey, second step, determine jet destroy the soil body the limit cut distance, 3rd step, determine the reduction coefficient considering nozzle translational speed, 4th step, the limit destroying the soil body based on jet cut the reduction coefficient that Distance geometry considers nozzle translational speed, for the construction of single pipe method, double tube method and tri-tube method high-pressure rotary-spray, determine the diameter of high-pressure rotary jet grouting pile.This method overcomes the parameter existed in existing method and lacks the shortcoming and defect such as physical significance, prediction deviation is large, stake footpath influence factor is considered entirely, range of application is narrow, realizes accurately determining of single pipe method, double tube method and tri-tube method high-pressure rotary jet grouting pile diameter.

Description

Consider the high-pressure rotary jet grouting pile method for determining diameter of whole construction parameter and soil strength variation

Technical field

What the present invention relates to is a kind of method of construction engineering technical field, specifically a kind of single tube, double pipe and triple-pipe high pressure jet grouting stake method for determining diameter simultaneously considering whole construction parameter and soil strength variation.

Background technology

Along with the development of China's civil engineering construction, High-pressure Spiral Spray Technology is widely used, as construction of tunnel, base pit engineering as the relatively simple method for processing foundation of a kind of constructing operation.High-pressure Spiral Spray Technology is that the soil body is cut in the shower nozzle ejection high-speed jet rotated, and then cement paste is mixed to form cement-soil mixture with the part soil body cut, and through chemical reaction Post RDBMS after a while, finally forms high-pressure rotary jet grouting pile.Because high-pressure rotary-spray formation of pile is an extremely complicated process, thus the prediction of its expanded diameter is the difficult problem of High-pressure Spiral Spray Technology design stage always.Traditional high-pressure rotary jet grouting pile method for determining diameter is the test value of the high-pressure rotary jet grouting pile diameter obtained based on digging in-situ and the empirical approach summing up out, namely has following two classes: (1) empirical formula method completely; (2) half theoretical semi-empirical approach.Calculating parameter in complete empirical formula method is obtained by indoor experimental data regression analysis by Japanese engineers, both well parametric technique was not determined, put forward parameter and lack again comparatively clear and definite physical significance, the high-pressure rotary-spray engineering design of China can not be directly applied to.It is theoretical that half theoretical semi-empirical approach then resists jet erosion based on circular free turbulent jet theory and the soil body, generally using the diameter of the scope of damaged for the jet erosion soil body as high-pressure rotary jet grouting pile, but the stake footpath influence factor that the method is considered is comprehensive not, and only can calculate the construction of single pipe method high-pressure rotary-spray, be difficult to be directly used in the diameter determining double pipe and triple-pipe high pressure jet grouting stake.

Retrieve rear discovery to existing document, Chinese invention patent application number is CN201110314616.2, denomination of invention: based on the high-pressure rotary jet grouting pile method for determining diameter of circular free turbulent jet theory.Although this patent proposes consider that the high-pressure rotary-spray construction technology of soil condition and rotary-spraying construction parameter generates the method for determining diameter of reinforcing body, but the Jet Axis that this patent proposes calculates applicable to attenuation factor to single pipe method high-pressure rotary jet grouting pile diameter, and to double tube method and the construction of tri-tube method high-pressure rotary-spray, adopt this axial attenuation factor to calculate and can not obtain correct stake footpath predicted value.Dabbagh etc. to be proved fine particle content and the increase of action time during soil layer characteristic velocity is along with soil at the article " Soilerosionbyacontinuouswaterjet " to deliver for 2002 and increase by laboratory test, but only choose fine particle content to calculate soil layer feature breakdown speed, do not consider that high-pressure rotary jet grouting pile expanded diameter reduces along with the particle diameter reduction of soil particle, soil layer feature breakdown speed increases with the reduction of radii of soil particles.By test, Yoshida etc. prove that high-speed jet can increase to some extent to the increase of the cutting distance of the soil body along with injecting time in the article " Effectofnozzletraverserateandnumberofpassesoncuttingsoil utilizingwaterjetforwiderapplication " to deliver for 1991, and do not consider to determine two factor nozzle translational speeds of jet injecting time and repeat injecting times cuts distance impact on the limit.

Summary of the invention

For the defect in existing method, the object of this invention is to provide a kind of high-pressure rotary jet grouting pile method for determining diameter simultaneously considering whole construction parameter and soil strength variation, the method overcome the parameter existed in existing method and lack the shortcoming and defect such as physical significance, prediction deviation is large, stake footpath influence factor is considered entirely, range of application is narrow, realize accurately determining of single pipe method, double tube method and tri-tube method high-pressure rotary jet grouting pile diameter.

In order to realize above object, the invention provides a kind of high-pressure rotary jet grouting pile method for determining diameter simultaneously considering whole construction parameter and soil strength variation, described method is realized by following steps:

The first step, construction field geology survey, concrete:

1) fetched earth in the region needed reinforcement at the construction field (site), record the relative density of soil sample, moisture content, density, and then according to the relative density of the soil body, moisture content and density, compartmentalize soil is carried out to the region needed reinforcement;

2) undrained shear strength or the grittiness soil classifiction of cohesive soil is obtained by test;

3) particle size analysis is carried out to soil sample, obtain its particle composition, and make particle size distribution figure;

Second step, determine jet destroy the soil body the limit cut distance, concrete:

In high-pressure rotary-spray construction, suppose that the fluid that nozzle sprays is identical with the character of surrounding fluid, then high-pressure rotary-spray construction high speed fluid meets circular free turbulent jet theory from the velocity pattern after nozzle ejection, speed on jet axis is along with the increase meeting constantly decay of the distance apart from spout, theoretical according to damage of soil body, when decaying to soil body critical slope langth speed, the soil body no longer destroys, now corresponding ultimate range is the limit and cuts distance, and the limit cutting distance that jet destroys the soil body can be determined by following formula:

$x_L=\mathrm{\α}\frac{d_0{v}_0}{v_L}$

In formula: x _lthe limit destroying the soil body for jet cuts distance;

α is axial attenuation factor, by second step 1) determine;

D ₀for nozzle diameter, can obtain by reading sprinkler design figure;

V ₀for jet nozzle muzzle velocity, by second step 2) determine;

V _lfor soil body critical slope langth speed, by second step 3) determine;

1) axial attenuation factor is determined

Described axial attenuation factor refers to the ability that the flow velocity on jet axis is decayed along jet length.Single pipe method adopts merely cement paste jet to carry out cutting soil, and this axial attenuation factor can be obtained by the coefficient of the axial attenuation factor when jet is cement paste jet with consideration water and cement paste two kinds of different jet nature differences.And double tube method and tri-tube method adopt the cement paste jet cutting soil of compressed air parcel, compressed-air actuated effect slow down the ability that jet is decayed vertically, be equivalent to increase the simple axial attenuation factor adopting cement paste jet to carry out cutting soil, the present invention proposes to consider that the dimensionless factor of compressed-air actuated increase effect represents compressed-air actuated effect.Following formula is met for the axial attenuation factor of different high-pressure rotary-spray construction methods:

1. single pipe method: $\mathrm{\α}={\mathrm{\α}}_g=\frac{{\mathrm{\α}}_w}{B}$

2. double tube method and tri-tube method:

In formula: α _gfor water under high pressure mud Jet Axis is to attenuation factor;

α _wfor the axial attenuation factor when jet is water, be generally taken as 16;

B is the coefficient considering water and cement paste two kinds of different jet nature differences;

ψ is the dimensionless factor considering compressed air increase effect;

Preferably, the coefficient of described consideration water and cement paste two kinds of different jet nature differences can by following formulae discovery:

$B=\sqrt{\frac{{\mathrm{\μ}}_g/{\mathrm{\ρ}}_g}{{\mathrm{\μ}}_w/{\mathrm{\ρ}}_w}}$

In formula: μ _gfor the apparent viscosity of cement paste;

ρ _gfor the density of cement paste;

μ _wfor the apparent viscosity of water, be generally taken as 0.001Pas;

ρ _wfor the density of water, be generally taken as 1000kg/m ³;

More preferably, the apparent viscosity of described cement paste can by following formulae discovery:

μ _g＝0.007(W) ^-2

In formula: W is the water/binder ratio of cement paste, can be obtained by Construction Design Schemes;

More preferably, the density of described cement paste can by following formulae discovery:

${\mathrm{\ρ}}_g=\frac{{\mathrm{\ρ}}_w{\mathrm{\ρ}}_c(1+W)}{{\mathrm{\ρ}}_w+{\mathrm{W\ρ}}_c}$

In formula: ρ _cfor the density of cement, be generally taken as 3150kg/m ³;

Preferably, the dimensionless factor of described consideration compressed air increase effect can by following formulae discovery:

$\mathrm{\ψ}=1+0.054\frac{p_a}{p_{\mathrm{atm}}}$

In formula: p _afor blast injection pressure, can be obtained by Construction Design Schemes;

2) jet nozzle muzzle velocity is determined

Described jet nozzle muzzle velocity is the speed that cement paste has when nozzle sprays, can determine by following formula:

$v_0=\frac{4Q}{\mathrm{M\π}{d_0}^2}$

In formula: Q, for spraying fluid flow, can be obtained by Construction Design Schemes;

M is nozzle number, can obtain by reading sprinkler design figure;

3) soil body critical slope langth speed is determined

Described soil body critical slope langth speed refers to that jet can make the soil body produce the minimum speed destroyed, can by following formulae discovery:

$v_L=\mathrm{\β}{\left(\frac{q_u}{p_{\mathrm{atm}}}\right)}^k$

In formula: p _atmit is a standard atmospheric pressure value;

Q _ufor soil body resistance, for cohesive soil: q _u=2c _u, for sandy soil: q _u=2 τ _f, c _uand τ _fby the first step 2) obtain;

K is empirical coefficient, is generally taken as 0.5;

β is soil layer characteristic velocity;

Preferably, soil layer characteristic velocity increases along with the increase of fine particle content in soil.The result of high-pressure rotary-spray field trial also shows: for same construction parameter and soil strength, and the particle diameter of soil particle is less, and expanded diameter is also less, and that is soil layer characteristic velocity increases along with the reduction of radii of soil particles.The present invention chooses fine particle content and soil particle average grain diameter represents the impact of grain composition on β, can determine by following piecewise function:

$\mathrm{\β}=\left\{\begin{array}{c}{b}_0{\left(\frac{M_c}{100}\right)}^{b_1}{\left(\frac{D_{50}}{D_f}\right)}^{b_2},5\≤M_c\≤100\\ b_0{\left(\frac{5}{100}\right)}^{b_1}{\left(\frac{D_{50}}{D_f}\right)}^{b_2},0\≤M_c\≤5\end{array}\right.$

In formula: M _cfor fine grained in soil (particle diameter is less than 75 μm) content, the particle size distribution figure that can be made up of the first step reads;

D ₅₀for soil particle average grain diameter, the particle size distribution figure that can be made up of the first step reads;

D _ffor fine grained particle diameter boundary value, be taken as 0.075mm;

B ₀, b ₁and b ₂for parameter, determined by the method doing the regression analysis again of laboratory test that fine particle content and soil particle average grain diameter in soil affect soil layer characteristic velocity, be generally taken as b respectively ₀=2.87, b ₁=0.4 and b ₂=-0.4;

3rd step, determine to consider the reduction coefficient of injecting time, concrete:

High-speed jet can increase to some extent to the increase of the cutting distance of the soil body along with injecting time, if injecting time long enough, can there is a limit and cut distance.Consider the detailed process of high-pressure rotary-spray construction, determine that the factor of jet injecting time mainly contains two: nozzle translational speed and repetition injecting times.Usually, nozzle translational speed is less, repeats injecting times more, and the final high-pressure rotary jet grouting pile diameter formed is also larger.For the calculating of high-pressure rotary jet grouting pile expanded diameter, can think because injecting time is limited and cause the limit to cut the reduction of distance, the present invention proposes one and considers that the reduction coefficient of nozzle translational speed is to calculate this reduction effect, and this coefficient can be determined by following formula:

$\mathrm{\η}=a_0{\left(\frac{v_{m0}}{v_m}\right)}^{a_1}{N}^{a_2}$

In formula: η is the reduction coefficient considering nozzle translational speed;

V _mfor the translational speed of nozzle, by the 3rd step 1) determine;

N is repetition injecting times, by the 3rd step 2) determine;

V _m0for making a paricular value acquired by formula nondimensionalization, be generally taken as 0.071m/s;

A ₀, a ₁and a ₂for parameter, by do about nozzle translational speed and repeat injecting times the method for high-speed jet on the regression analysis again of the laboratory test of the cutting of soil body distance impact determined, be generally taken as a respectively ₀=0.09, a ₁=0.14 and a ₂=0.2;

1) translational speed of nozzle is determined

The translational speed of described nozzle be nozzle along the speed of boring spray boom tangential direction, can by following formulae discovery:

$v_m=\sqrt{{\left(\mathrm{\π}{R}_s{D}_r\right)}^2+v_s^2}$

In formula: R _sfor rotary speed, can be obtained by Construction Design Schemes;

D _rfor boring spray boom diameter, for single tube, double pipe and triple-pipe high pressure jet grouting engineering method, value is respectively 60mm, 76mm and 90mm;

V _sfor hoisting velocity, can be obtained by Construction Design Schemes;

2) repetition injecting times is determined

Described repetition injecting times is that in high-pressure rotary-spray construction process, cement paste repeats the number of times of jetting nozzle, can by following formulae discovery:

$N=M\frac{R_s}{v_s}\mathrm{\Δ}{S}_t$

In formula: Δ St be hoistway every, be generally taken as 5cm;

4th step, determine the diameter of high-pressure rotary jet grouting pile, concrete:

The limit destroying the soil body based on jet cuts the reduction coefficient that Distance geometry considers nozzle translational speed, for the construction of single pipe method, double tube method and tri-tube method high-pressure rotary-spray, and the diameter by following formula determination high-pressure rotary jet grouting pile:

$D_0=2\mathrm{\η}{x}_L+D_r=2a_0\mathrm{\α}{N}^{a_2}\frac{d_0{v}_0}{x_L}{\left(\frac{v_{m0}}{v_m}\right)}^{a_1}+D_r$

In formula: D ₀for the rotary churning pile diameter calculated;

η is the reduction coefficient considering nozzle translational speed, is obtained by second step;

X _lthe limit destroying the soil body for jet cuts distance, is obtained by the 3rd step;

The present invention passes through compared with prior art, has following beneficial effect:

The inventive method considers whole construction parameter and soil strength variation simultaneously, realizes accurately determining of high-pressure rotary jet grouting pile diameter; The present invention proposes nozzle translational speed and repeats injecting times cuts distance influence coefficient to the limit, soil particle average grain diameter is considered in the calculating of soil layer feature breakdown speed, and corresponding Jet Axis is proposed to attenuation factor for 3 kinds of basic High-pressure Spiral Spray Technologies, the factor considered is more thorough, and it is more accurate to judge; The present invention can be used for accurately determining of single pipe method, double tube method and tri-tube method high-pressure rotary jet grouting pile diameter; The inventive method is simple, and the degree of accuracy is high, and applicability is strong.

Accompanying drawing explanation

Fig. 1 the present invention adopts the soil layer particle size distribution figure of single pipe method high-pressure rotary-spray construction embodiment.

Fig. 2 the present invention adopts measured diameter and the calculated diameter Comparative result of single pipe method, double-tube method and three tube method high-pressure rotary-spray embodiments.

Detailed description of the invention

Below in conjunction with specific embodiment, the present invention is described in detail.Following examples will contribute to those skilled in the art and understand the present invention further, but not limit the present invention in any form.It should be pointed out that to those skilled in the art, without departing from the inventive concept of the premise, some distortion and improvement can also be made.These all belong to protection scope of the present invention.The operation be not particularly illustrated in the present embodiment, carries out with reference to the method provided in summary of the invention, does not repeat them here.

The present embodiment illustrates high-pressure rotary jet grouting pile method for determining diameter for adopting single pipe method High-pressure Spiral Spray Technology strengthening stratum.Described in specific as follows:

Certain single pipe method subsidence pressure circle spray reinforcement soil layer is positioned at Italian Naples city, and set 7 high-pressure rotary jet grouting piles altogether, designing pile length 10m, stake top is positioned at below earth's surface 2m, is positioned at below earth's surface 12m at the bottom of stake.Be excavated to underground 8m after having constructed and measure the diameter forming rotary churning pile.The present embodiment is chosen a wherein pile and is calculated in detail.

Step one, construction field geology survey, concrete:

1) fetched earth in the region needed reinforcement at the construction field (site), record the relative density of soil sample, moisture content, density, and then according to the relative density of the soil body, moisture content and density, compartmentalize soil is carried out to the region needed reinforcement;

2) undrained shear strength or the grittiness soil classifiction of cohesive soil is obtained by test.

3) particle size analysis is carried out to soil sample, obtain its particle composition, and make particle size distribution figure.

In the present embodiment, use heavy wall borrow equipment, fetched earth from ground to 1.5 of the projected depth of stake times in the region needed reinforcement at the construction field (site).

In the present embodiment, recorded the relative density of soil sample by bottle method.Described bottle method follows earthwork test rule, tests determined soil body relative density values by picknometer.

In the present embodiment, recorded the moisture content of soil sample by oven drying method.Described oven drying method is the wet soil quality first claiming fritter undisturbed soil sample, is then placed in baking oven to maintain 105 DEG C and dry to constant weight, then claims dry ground quality, and wet, the difference of dry ground quality and the ratio of dry ground quality, be exactly soil's water content, this test method is called oven drying method.

In the present embodiment, recorded the density of soil sample by core cutter method.Described core cutter method is placed on the undisturbed soil sample face of scabbling with an annulus cutter (blade is downward), slowly to prune the soil of cutting ring periphery, limit chamfered edge pressure, make in the full cutting ring of soil sample pressure of maintenance native state, claim to obtain quality of soil sample in cutting ring, the ratio of trying to achieve it and cutting ring volume is density value, and this test method is called core cutter method.

In the present embodiment, on-the-spot standard penetration test is adopted to obtain undrained shear strength or the grittiness soil classifiction of cohesive soil.Described standard penetration test refers to: hammer into shape by the punching of 63.5kg at the scene, freely fall with the distance that falls of 76cm, the standard penetrometer with small-sized soil sample barrel of length 51cm, external diameter 5.1cm, internal diameter 3.49cm is squeezed in soil, the blow counts squeezing into 30cm is Standard penetration test blow count, and this process of the test is called standard penetration test.

In the present embodiment, the undrained shear strength of described cohesive soil can by following formulae discovery:

c _u＝(4.4-6)N _SPT

In formula: c _ufor undrained shear strength;

N _sPTfor Standard penetration test blow count;

Described grittiness soil classifiction can by following formulae discovery:

τ _f＝σ' _vtanφ'

${\mathrm{\φ}}^{\′}=\sqrt{20\frac{N_{\mathrm{SPT}}}{\sqrt{{\mathrm{\σ}}_v^{\′}/98}}}+20$

In formula: τ _ffor shear strength;

σ ' _vfor the effective stress of soil;

φ ' is effective angle of friction;

In the present embodiment, adopt laser particle analyzer to carry out sizing assay test to the soil sample of fetching, obtain its particle composition, and make particle size distribution figure.

Finally obtain: the relative density of the construction area soil body is 2.66, and moisture content is 20% ~ 40%, and density is 1800kg/m ³.Field geology situation: topmost one deck (0.0 ~ 1.5m) is back fill course; Its lower floor (1.5 ~ 14m) silty sand ground; Lower floor (14 ~ 29m) is farinose argillic horizon again.The construction area soil body is sandy soil, and Standard penetration test blow count is N _sPT=8, effective angle of inner friction φ '=35 °, the effective stress σ ' of soil _v=55kPa, shear strength τ _f=38.5kPa.The particle size distribution of soil as shown in Figure 1.

Step 2, determine that the limit that jet destroys the soil body cuts distance, concrete:

With reference to the explanation in summary of the invention, according to high-pressure rotary-spray construction design scheme, the water/binder ratio W=1:1 of cement paste, the density p of cement _c=3150kg/m ³, the density p of water _w=1000kg/m ³, the apparent viscosity μ of water _w=0.001Pas; Axial attenuation factor α when jet is water _wget 16, then the apparent viscosity μ of cement paste _g=0.007, the density p of cement paste _g=1518.1kg/m ³, consider coefficient B=2.14 of water and cement paste two kinds of different jet nature differences.Water under high pressure mud Jet Axis is to attenuation factor α _g=7.47, then α=7.47.

According to high-pressure rotary-spray construction design scheme, spray the flow Q=0.00138m of fluid ³/ s, according to sprinkler design figure, nozzle number M=2, nozzle diameter d ₀=0.002m, jet nozzle muzzle velocity v ₀=219.6m/s.

Fine particle content M in soil can be obtained according to soil layer particle size distribution figure _c=20%, soil particle average grain diameter D ₅₀=0.112mm, fine grained particle diameter boundary value D _f=0.075mm, b ₀=2.87, b ₁=0.4, b ₂=-0.4, then soil layer characteristic velocity β=1.28.A standard atmospheric pressure p _atmget 101.325kPa, soil body resistance q _u=77kPa, then soil body critical slope langth speed v _l=1.12m/s.

According to the above-mentioned water under high pressure mud Jet Axis calculated to attenuation factor α, jet nozzle muzzle velocity v ₀, soil body critical slope langth speed v _lcan determine that jet destroys the limit cutting distance x of the soil body _l=2.93m.

Step 3, determine to consider the reduction coefficient of injecting time, concrete:

According to Construction Design Schemes, rotary speed R _s=15rpm, bores spray boom diameter D _r=60mm, hoisting velocity v _s=0.00571m/s, the then movement speed v of nozzle _m=2.82m/s.

According to Construction Design Schemes, time interval Δ St=5cm, repeats times N=262.7 of spraying.

According to the movement speed v of the above-mentioned nozzle calculated _mwith the times N repeating to spray, a ₀=0.09, a ₁=0.14, a ₂=0.2, reduction coefficient η=0.164 considering injecting time can be determined.

Step 4, determine the diameter of high-pressure rotary jet grouting pile, concrete:

According to the limit cutting distance x of the jet destruction soil body that step 2 obtains _lthe reduction coefficient η of the consideration injecting time obtained with step 3 can determine the diameter D of this high-pressure rotary jet grouting pile ₀=1.02m.This measured diameter is 1.11m, and the comparison diagram of calculated diameter and measured diameter as shown in Figure 2.

The present embodiment also calculates the rotary churning pile that double tube method and tri-tube method High-pressure Spiral Spray Technology strengthening stratum are formed, and detailed step is similar to above-mentioned single pipe method, does not repeat them here.Double-tube method subsidence pressure circle spray reinforcement soil layer is positioned at Izmir city of Turkey, and set 4 high-pressure rotary jet grouting piles altogether, designing pile length 6m, stake top is positioned at earth's surface, is positioned at below earth's surface 6m at the bottom of stake, is excavated to underground 3m and measures the diameter forming rotary churning pile after having constructed.Three tube method subsidence pressure circle spray reinforcement soil layers are positioned at Mianeh town, the Iranian northwestward, set 6 high-pressure rotary jet grouting piles altogether, not etc., stake top is not positioned at earth's surface to designing pile length 5m to 10.5m, the stake end, is positioned at below earth's surface 5m to 10.5m, is excavated to underground 3m to 5m and measures the diameter forming rotary churning pile after having constructed.

The single pipe method that the embodiment of the present invention is determined, the comparison diagram of double tube method and tri-tube method high-pressure rotary-spray diameter and measured value are as shown in Figure 2, can find out that the present embodiment can determine the high-pressure rotary jet grouting pile diameter that three kinds of basic churning engineering methods are formed accurately, former method of comparing is more scientific, more accurate, brings great convenience to the working design of High-pressure Spiral Spray Technology.

Above specific embodiments of the invention are described.It is to be appreciated that the present invention is not limited to above-mentioned particular implementation, those skilled in the art can make various distortion or amendment within the scope of the claims, and this does not affect flesh and blood of the present invention.

Claims (1)

1. consider a high-pressure rotary jet grouting pile method for determining diameter for whole construction parameter and soil strength variation, it is characterized in that, comprise the steps:

The first step, construction field geology survey:

1) fetched earth in the region needed reinforcement at the construction field (site), record the relative density of soil sample, moisture content, density, and then according to the relative density of the soil body, moisture content and density, compartmentalize soil is carried out to the region needed reinforcement;

2) undrained shear strength or the grittiness soil classifiction of cohesive soil is obtained by test;

3) particle size analysis is carried out to soil sample, obtain its particle composition, and make particle size distribution figure;

Second step, determine jet destroy the soil body the limit cut distance, determine by following formula:

$x_L=\mathrm{\α}\frac{d_0{v}_0}{v_L}$

In formula: x _lthe limit destroying the soil body for jet cuts distance; α is axial attenuation factor; d ₀for nozzle diameter, obtain by reading sprinkler design figure; v ₀for jet nozzle muzzle velocity; v _lfor soil body critical slope langth speed;

3rd step, determine the reduction coefficient considering nozzle translational speed, determine by following formula:

$\mathrm{\η}=a_0{\left(\frac{v_{m0}}{v_m}\right)}^{a_1}{N}^{a_2}$

In formula: η is the reduction coefficient considering nozzle translational speed; v _mfor the translational speed of nozzle; N is for repeating injecting times; v _m0for making a paricular value acquired by formula nondimensionalization, be taken as 0.071m/s; a ₀, a ₁and a ₂for parameter, by do about nozzle translational speed and repeat injecting times the method for high-speed jet on the regression analysis again of the laboratory test of the cutting of soil body distance impact determined, be taken as a respectively ₀=0.09, a ₁=0.14 and a ₂=0.2;

4th step, determine the diameter of high-pressure rotary jet grouting pile:

The limit destroying the soil body based on jet cuts the reduction coefficient that Distance geometry considers nozzle translational speed, for the construction of single pipe method, double tube method and tri-tube method high-pressure rotary-spray, and the diameter by following formula determination high-pressure rotary jet grouting pile:

$D_0=2{\mathrm{\ηx}}_L+D_r=2a_0{\mathrm{\αN}}^{a_2}\frac{d_0{v}_0}{v_L}{\left(\frac{v_{m0}}{v_m}\right)}^{a_1}+D_r$

In formula: D ₀for the rotary churning pile diameter calculated; η is the reduction coefficient considering nozzle translational speed; x _lthe limit destroying the soil body for jet cuts distance, D _rfor boring spray boom diameter;

Described axial attenuation factor α meets following formula:

1. single pipe method: $\mathrm{\α}={\mathrm{\α}}_g=\frac{{\mathrm{\α}}_w}{B}$

2. double tube method and tri-tube method:

In formula: α _gfor water under high pressure mud Jet Axis is to attenuation factor; α _wfor the axial attenuation factor when jet is water; B is the coefficient considering water and cement paste two kinds of different jet nature differences; ψ is the dimensionless factor considering compressed air increase effect;

The coefficient B of described consideration water and cement paste two kinds of different jet nature differences is by following formulae discovery:

$B=\sqrt{\frac{{\mathrm{\μ}}_g/{\mathrm{\ρ}}_g}{{\mathrm{\μ}}_w/{\mathrm{\ρ}}_w}}$

In formula: μ _gfor the apparent viscosity of cement paste; ρ _gfor the density of cement paste; μ _wfor the apparent viscosity of water; ρ _wfor the density of water;

The apparent viscosity μ of described cement paste _gby following formulae discovery:

μ _g＝0.007(W) ^-2

In formula: W is the water/binder ratio of cement paste, is obtained by Construction Design Schemes;

The density of described cement paste is by following formulae discovery:

${\mathrm{\ρ}}_g=\frac{{\mathrm{\ρ}}_w{\mathrm{\ρ}}_c(1+W)}{{\mathrm{\ρ}}_w+{\mathrm{W\ρ}}_c}$

In formula: ρ _cfor the density of cement;

The dimensionless factor of described consideration compressed air increase effect is by following formulae discovery:

$\mathrm{\ψ}=1+0.054\frac{p_a}{p_{atm}}$

In formula: p _afor blast injection pressure, obtained by Construction Design Schemes; p _atmit is a standard atmospheric pressure value;

Described jet nozzle muzzle velocity is the speed that cement paste has when nozzle sprays, determines by following formula:

$v_0=\frac{4Q}{{{\mathrm{M\πd}}_0}^2}$

In formula: Q, for spraying fluid flow, is obtained by Construction Design Schemes; M is nozzle number;

Described soil body critical slope langth speed refers to that jet can make the soil body produce the minimum speed destroyed, by following formulae discovery:

$v_L=\mathrm{\β}{\left(\frac{q_u}{p_{atm}}\right)}^k$

In formula: p _atmit is a standard atmospheric pressure value; q _ufor soil body resistance, for cohesive soil: q _u=2c _u, for sandy soil: q _u=2 τ _f, c _ufor undrained shear strength, τ _ffor shear strength; K is empirical coefficient, gets 0.5; β is soil layer characteristic velocity;

The undrained shear strength of described cohesive soil is by following formulae discovery:

c _u＝(4.4-6)N _SPT

In formula: c _ufor undrained shear strength; N _sPTfor Standard penetration test blow count;

Described grittiness soil classifiction is by following formulae discovery:

τ _f＝σ' _vtanφ'

${\mathrm{\φ}}^{\′}=\sqrt{20\frac{N_{SPT}}{\sqrt{{\mathrm{\σ}}_v^{\′}/98}}}+20$

In formula: τ _ffor shear strength; σ ' _vfor the effective stress of soil; φ ' is effective angle of friction;

Choose fine particle content and soil particle average grain diameter represents the impact of grain composition on β, determine by following piecewise function:

$\mathrm{\β}=\left\{\begin{array}{c}{b}_0{\left(\frac{M_c}{100}\right)}^{b_1}{\left(\frac{D_{50}}{D_f}\right)}^{b_2},5\≤M_c\≤100\\ b_0{\left(\frac{5}{100}\right)}^{b_1}{\left(\frac{D_{50}}{D_f}\right)}^{b_2},0\≤M_c\≤5\end{array}\right.$

In formula: M _cfor fine particle content in soil, the particle size distribution figure be made up of the first step reads; D ₅₀for soil particle average grain diameter, the particle size distribution figure be made up of the first step reads; D _ffor fine grained particle diameter boundary value, be taken as 0.075mm; b ₀, b ₁and b ₂for parameter, determined by the method doing the regression analysis again of laboratory test that fine particle content and soil particle average grain diameter in soil affect soil layer characteristic velocity, be taken as b respectively ₀=2.87, b ₁=0.4 and b ₂=-0.4;

The translational speed of described nozzle is the speed of nozzle along brill spray boom tangential direction, by following formulae discovery:

$v_m=\sqrt{{\left({\mathrm{\πR}}_s{D}_r\right)}^2+v_s^2}$

In formula: R _sfor rotary speed, obtained by Construction Design Schemes;

D _rfor boring spray boom diameter, for single tube, double pipe and triple-pipe high pressure jet grouting engineering method, value is respectively 60mm, 76mm and 90mm;

V _sfor hoisting velocity, obtained by Construction Design Schemes;

Described repetition injecting times N is the number of times that in high-pressure rotary-spray construction process, cement paste repeats jetting nozzle, by following formulae discovery:

$N=M\frac{R_s}{v_s}{\mathrm{\ΔS}}_t$

In formula: M is nozzle number, Δ St be hoistway every, be taken as 5cm; R _sfor rotary speed; v _sfor hoisting velocity.